Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B

Average Error: 1.3 → 1.3

Time: 13.9s

Precision: 64

Math

\[x + y \cdot \frac{z - t}{a - t}\]

↓

\[x + y \cdot \frac{z - t}{a - t}\]

C

double f(double x, double y, double z, double t, double a) {
        double r427570 = x;
        double r427571 = y;
        double r427572 = z;
        double r427573 = t;
        double r427574 = r427572 - r427573;
        double r427575 = a;
        double r427576 = r427575 - r427573;
        double r427577 = r427574 / r427576;
        double r427578 = r427571 * r427577;
        double r427579 = r427570 + r427578;
        return r427579;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r427580 = x;
        double r427581 = y;
        double r427582 = z;
        double r427583 = t;
        double r427584 = r427582 - r427583;
        double r427585 = a;
        double r427586 = r427585 - r427583;
        double r427587 = r427584 / r427586;
        double r427588 = r427581 * r427587;
        double r427589 = r427580 + r427588;
        return r427589;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.3
Target	0.5
Herbie	1.3

\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241069024247453646278348229 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

1. Initial program 1.3

   \[x + y \cdot \frac{z - t}{a - t}\]

2. Final simplification 1.3

   \[\leadsto x + y \cdot \frac{z - t}{a - t}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.50808486055124107e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.8944268627920891e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

  (+ x (* y (/ (- z t) (- a t)))))